Stochastic Properties of Daily Temperature in Rivers

Some stochastic properties of the daily range of water temperature variations in rivers, most of which are located in the central part of the United States, were analyzed using data published by the U.S. Geological Survey. It was found that the water temperature variation follows quite closely the patterns of air temperature variation when the river is not subjected to freezing. Freezing tends to inhibit the water temperature variation, and the degree of daily temperature variation diminishes as the daily mean temperature approaches 0°C. As a result the daily range of water temperature variation of a freezing river is highly correlated with daily mean water temperature. Some aspects of auto-regression and cross-regression models were reviewed and applied. An air-water temperature response coefficient was found to correlate well with a dimensionless number representing the ratio of the characteristic period of air temperature variation and the characteristic time scale of heat transfer in a river.